7. The perimeter of a circle of diameter 10 cm is-
(a) 30.4 cm. (b) 30.14 cm
(c) 31.4 cm. (d) 30.01 cm.
(Take π = 3.14)
\(\qquad\qquad\qquad\boxed{\bf\:\:{(c) \: 31.4 \: cm \: ans \: }}\)
Explanation -:
The diameter is = 10 cm
( Take π = 3.14 )
\( \\ \: \tt :\implies \: 10 \: \times 3.14 \\ \\ 31.4 \: ans\)
More Information -:
Area of circle= πr² Circumference= 2 πr π = 22/7 or 3.14 ( approx )Annulas = π(R² - r ²)Tristan wants to ride his bicycle 27 miles this week. He has already ridden 9 miles. If
he rides for 6 more days, which tape diagram could be used to represent the context if
2 represents the average number of miles he would have to ride to meet his goal?
Answer:
he would have to ride for 3 miles each of the six days left to meet his goal
Step-by-step explanation:
Is (-1,3) a solution to the system: y=4x+1 Y=x - 2
Answer: no the solution is (-1,-3)
Step-by-step explanation:
Step-by-step explanation:
step 1. a solution to a 2 variable system must work for both equations
step 2. y = 4x + 1, 3 = 4(-1) + 1, 3 = -4 + 1. no.
step 3. answer: no.
Sean wants to build a treehouse. They have a 13-foot ladder that must
be propped diagonally against the tree. If the base of the ladder is 5
feet from the bottom of the tree, how high will the tree house be off the
ground? Round your answer to the nearest tenth.
Answer:
im sorry i need the poonts have a good day
WILL GIVE BRAINLIEST!!!!!!!!!!
A sandcastle can be modeled with four 6-inch-tall square prisms, one on top of the other, as shown in the figure below.
The base of the bottom prism has a side length of 30 inches, and the base of each of the other three prisms has a side length 7 inches less than the side length of the base of the prism below it. What is the volume of the sand castle?
Answer:
A 2808
Step-by-step explanation:
From top to bottom
The top one is 9
Second layer is 16
Third is 23
Bottom is 30
I did 9 x 6, 16 x 6, 23 x 6, 30 x 6 = 54, 96, 138, 180
Added all of them up and got 468 then I times it by 6 and got 2808
Heyo! ;D
The volume of the sandcastle above is 10,596 cubic inches.
Hope this helped! If so, please lmk! Tysm and good luck!
If you look at someone contemptuously, what do you think of them?
You want to talk to them.
You don’t like them.
You don’t know them.
You feel bad for them.
Answer:
You don't like them
Step-by-step explanation:
definition: contemptuously
ADVERB
contemptuously (adverb)
in a scornful way that shows disdain.
"he contemptuously dismisses his son's work"
Al released his balloon from the 10-yard line, and it landed at the 16-yard line. If the ball reached a height of 27 yards, what equation represents the path of his toss?
The equation of the path of the parabola is y = a(x - 13)² + 27
Given data ,
To represent the path of Al's toss, we can assume that the path is a parabolic trajectory.
The equation of a parabola in vertex form is given by:
y = a(x - h)² + k
where (h, k) represents the vertex of the parabola
Now , the balloon was released from the 10-yard line and landed at the 16-yard line, we can determine the x-values for the vertex of the parabola.
The x-coordinate of the vertex is the average of the two x-values (10 and 16) where the balloon was released and landed:
h = (10 + 16) / 2 = 13
Since the height of the balloon reached 27 yards, we have the vertex point (13, 27)
Now, let's substitute the vertex coordinates (h, k) into the general equation:
y = a(x - 13)² + k
Substituting the vertex coordinates (13, 27)
y = a(x - 13)² + 27
To determine the value of 'a', we need another point on the parabolic path. Let's assume that the highest point reached by the balloon is the vertex (13, 27).
This means that the highest point (13, 27) lies on the parabola
Substituting the vertex coordinates (13, 27) into the equation
27 = a(13 - 13)² + 27
27 = a(0) + 27
27 = 27
Hence , the equation representing the path of Al's toss is y = a(x - 13)² + 27, where 'a' can be any real number
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Four students did a 400 meter sprint relay. Henry's time was 51.10 seconds, Cathryn's time was 45.26 seconds, Grayson's time was 101.92 seconds, and Woody's time was 62.14 seconds. What was their total time?
260.42
Answer:
if you know why did you ask?
Step-by-step explanation:
please answer fast and quickly
Answer:
Blue
stay safe healthy and happy...Hello there I hope you are having an great day :) If you select a marble without looking which colour are you less likely to pick, All together there is 10 marbles.
Orange : 2/10
Black : 2/10
Green : 5/10
Blue: 1/10
The less Colour is Blue as there is only 1 Marble so it probably the less likely to be picked.
Hopefully that helps you :)
The percentage, P(t), of information memorized by Bridget is a function of the time, t,
in minutes, of the length of a lecture.
P(t) = t-t²
50
Bridget's friend wanted to determine the percentage memorized at various times and
evaluated the four values: P(40), P(50), P(60), P (70).
During what length of a lecture did Bridget memorize the most information?
40 min
O 50 min
60 min
O 70 min
Answer:
P(40) = 64, P(50) = 70, P(60) = 72,
P(70) = 70
60 minutes is correct.
Whay property is 5(x + 2) = 5x + 10
Answer:
Distributive property
Step-by-step explanation:
Answer:
Distributive property
Step-by-step explanation:
Please answer correctly !!!!!!!!!!!!!!! Will mark brainliest !!!!!!!!!!!!!!!!!!!!!
Answer:
I believe it is 14.
Step-by-step explanation:
Answer: The value of x is 14°
Step-by-step explanation:
Since line m is parallel to n, then then the two given angles will have the same measures. Meaning that 136 degrees has to equation (9x+10).
Set them to equal each other and solve for x.
9x + 10 = 136
- 10 -10
9x = 126
x= 14
What are 2 ways i could solve 7-(4p+3)=-3(p+2)-(2p+3)
Answer:
Simplifying
7 + -1(4p + 3) = -3(p + 2) + -1(2P + 3)
Reorder the terms:
7 + -1(3 + 4p) = -3(p + 2) + -1(2P + 3)
7 + (3 * -1 + 4p * -1) = -3(p + 2) + -1(2P + 3)
7 + (-3 + -4p) = -3(p + 2) + -1(2P + 3)
Combine like terms: 7 + -3 = 4
4 + -4p = -3(p + 2) + -1(2P + 3)
Reorder the terms:
4 + -4p = -3(2 + p) + -1(2P + 3)
4 + -4p = (2 * -3 + p * -3) + -1(2P + 3)
4 + -4p = (-6 + -3p) + -1(2P + 3)
Reorder the terms:
4 + -4p = -6 + -3p + -1(3 + 2P)
4 + -4p = -6 + -3p + (3 * -1 + 2P * -1)
4 + -4p = -6 + -3p + (-3 + -2P)
Reorder the terms:
4 + -4p = -6 + -3 + -2P + -3p
Combine like terms: -6 + -3 = -9
4 + -4p = -9 + -2P + -3p
Solving
4 + -4p = -9 + -2P + -3p
Solving for variable 'p'.
Move all terms containing p to the left, all other terms to the right.
Add '3p' to each side of the equation.
4 + -4p + 3p = -9 + -2P + -3p + 3p
Combine like terms: -4p + 3p = -1p
4 + -1p = -9 + -2P + -3p + 3p
Combine like terms: -3p + 3p = 0
4 + -1p = -9 + -2P + 0
4 + -1p = -9 + -2P
Add '-4' to each side of the equation.
4 + -4 + -1p = -9 + -4 + -2P
Combine like terms: 4 + -4 = 0
0 + -1p = -9 + -4 + -2P
-1p = -9 + -4 + -2P
Combine like terms: -9 + -4 = -13
-1p = -13 + -2P
Divide each side by '-1'.
p = 13 + 2P
Simplifying
p = 13 + 2P
Step-by-step explanation:
Find the equation for the plane through Po(2, -3, - 5) perpendicular to the following line. x=2+t, y=-3+5t, z= -3, -20 << Be sure to clearly show all work in order to receive full credit. Put your final answer in the form ax + by + cz = d. The equation of the plane is
5x - y - 13 = 0 is the equation of the plane
How to find the equation of a plane through a given point that is perpendicular to a given line in three-dimensional space?To find the equation of the plane, we need two pieces of information: a point on the plane, and the normal vector of the plane.
We are given a point on the plane: P0(2, -3, -5).
To find the normal vector of the plane, we need to use the fact that the plane is perpendicular to the given line. The direction vector of the line is <1, 5, 0>, since the line has parametric equations x=2+t, y=-3+5t, z=-3, and the vector <1, 5, 0> is the coefficient vector of the parameter t in these equations.
Any vector that is perpendicular to <1, 5, 0> will be a normal vector of the plane. One such vector is <5, -1, 0>, which we can verify by taking the dot product of this vector with <1, 5, 0>:
<5, -1, 0> · <1, 5, 0> = 5(1) + (-1)(5) + 0(0) = 0
Thus, the normal vector of the plane is <5, -1, 0>.
Now we can use the point-normal form of the equation of a plane:
ax + by + cz = d
where <a, b, c> is the normal vector of the plane, and (x, y, z) is any point on the plane. Substituting in the values we have:
5(x - 2) - 1(y + 3) + 0(z + 5) = 0
Simplifying:
5x - 10 - y - 3 = 05x - y - 13 = 0So the equation of the plane is:
5x - y - 13 = 0
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What is the area of this figure?
The area of the figure is given as follows:
100.56 mm².
How to obtain the area of the figure?The figure in this problem is composed as follows:
Rectangle of dimensions 4 mm and 12 mm.Rectangle of dimensions 2 mm and 7 mm.Rectangle of dimensions 4 mm and 12 - 7 = 5 mm.Rectangle of dimensions 3 mm and 2 mm.Semicircle of radius 2 mm.The areas for each region are given as follows:
Rectangle of dimensions 4 mm and 12 mm -> 4 x 12 = 48 mm²Rectangle of dimensions 2 mm and 7 mm -> 2 x 7 = 14 mm².Rectangle of dimensions 4 mm and 12 - 7 = 5 mm -> 4 x 5 = 20 mm².Rectangle of dimensions 3 mm and 2 mm -> 3 x 2 = 6 mm².Semicircle of radius 2 mm -> 3.14 x 2² = 12.56 mm².Hence the total area is of:
48 + 14 + 20 + 6 + 12.56 = 100.56 mm².
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How do you write a homogeneous system in parametric vector form?
A homogeneous system in parametric vector form:
(x1,x2,x3) = (s,s,-0.25s)
Parametric vector Form:
Any equation expressed as a parameter is a parametric equation. The general equation y = mx + b (where m and b are parameters) of a straight line in the form of a slope intersection is an example of a parametric equation. Example: one of the variables to t(x = t). Then we can rewrite this equation as y = t²+5.
So the set of parametric equations is x = t and y=t²+5.
According to the Question:
We are to solve them in parametric form.
X₁ + 2X₂ + 12X₃ = 0 ----------------------- (1)
2X₁ + X₂ + 12X₃ = 0 ----------------------- (2)
-X₁ + X₂ = 0 ----------------------- (3)
From equation 3 we get
x₁ = x₂
Substitute in 1 and 2 to get
3x₁ + 12x₃ = 0 and
3x₁ + 12x₃ = 0
Thus, we find these two equations are dependent. So we can have infinite solutions in parametric form only.
No unique solution is possible
Let x₁ = x₂ = s
Since 3x₁ +12x₃ = 0
x₁ = -4x₃
Or x₃ = -0.25s
So solution in parametric form is
(x1,x2,x3) = (s,s,-0.25s) for all real values.
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what is an equation of the line that passes through the points (3,0) and (-6,-3)
Step-by-step explanation:
given ponts,
(3,0)=(x1,y1)
(-6,-3)=(x2,y2)
we know,
Eqn of any line joining two points be,
(y-y1)={(y2-y1)/(x2-x1)}*(x-x1)
y-0={(-3-0)/(-6-3)}*(x-3)
y=(1/3)*(x-3)
y=(x-3)/3
3y=x-3
0=x-3y-3
x-3y-3=0
Therefore it is required eqn
Delia, Edwin and Freya share some money in the ratio 5 : 7 : 8. Freya’s share is £1600. How much money did they share?
Answer:
To find how much money they shared first find the total parts
Which is
5 + 7 + 8 = 20
Deila's share is
5 /20 × £1600
= 1/4 × £1600 = £ 400
Edwin's share is
7/ 20 ×£1600 = £560
Freya's share is
8/20 × £1600
= 2/5 × £1600 = £640
Hope this helps you
Answer:
£ 40,000
Step-by-step explanation:
Given that:
Freya receives 8 parts of the total amount
8 parts = £1600
this means, we can calculate 1 part:
8 parts = £1600
1 part =£1600/8 = £ 2000
Now, we are able to calculate the total share :
Total number of parts = 8 + 5 + 7 = 20
1 share = £2000
So, 20 shares = £40000
hope this helps,
Good Luck
Please mark brainiest
.Which of the following are among important considerations when using ANOVA to evaluate models?
(1) The ANOVA table is not the fitted model itself but rather an attempt to partition credit for the model's predictive power across the different variables.
(2) Interpreting the ANOVA table requires more subtlety when there is correlation among model predictors.
(3) There can only be one correct ANOVA table for any given model in the context of an observational study.
(4) All of the above (1, 2, and 3)
The correct answer is (4) All of the above (1, 2, and 3).
When using ANOVA to evaluate models, among the important considerations are:
The ANOVA table is not the fitted model itself but rather an attempt to partition credit for the model's predictive power across the different variables,
Interpreting the ANOVA table requires more subtlety when there is correlation among model predictors, and there can only be one correct ANOVA table for any given model in the context of an observational study.
Hence, the correct answer is (4) All of the above (1, 2, and 3).
ANOVA, short for Analysis of Variance, is a statistical method for comparing the means of two or more groups. It is utilized to compare whether there are any statistically significant differences between the group means.
The ANOVA table is not the fitted model itself but rather an attempt to partition credit for the model's predictive power across the different variables. Interpreting the ANOVA table requires more subtlety when there is correlation among model predictors.
There can only be one correct ANOVA table for any given model in the context of an observational study.
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A circle centered at the orgin has a radius of 13 units the terminal side of the angle 0 intercepts the circle in quadrant II at point c. the x coordinate of point c is -5 find the y- coordinate what is the value of sin 0
The y-coordinate of point C is -12, and the value of sinθ is -12/13.
How to find y-coordinate and sinθ given x-coordinate?We can begin by using the Pythagorean theorem to find the y-coordinate of point C.
Since the circle has a radius of 13 units, we know that the distance from the origin to point C is also 13 units. We can use the x-coordinate of point C to find the length of the horizontal leg of the right triangle formed by the origin, point C, and the x-axis.
The length of this leg is equal to the absolute value of the x-coordinate, so in this case it is 5 units. To find the length of the vertical leg, we can use the Pythagorean theorem:
y² + 5² = 13²
y² = 13² - 5²
y² = 144
y = ±12
Since point C is in quadrant II, the y-coordinate is positive. Therefore, the y-coordinate of point C is 12.
To find the value of sin(θ), we can use the fact that sin(θ) = opposite/hypotenuse. In this case, the opposite side is the y-coordinate of point C (which is 12), and the hypotenuse is the radius of the circle (which is 13).
So, sin(θ) = 12/13.
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Double integrals can only be calculated on rectangular domains. o True o False
The statement "Double integrals can only be calculated on rectangular domains" is false. Double integrals can be calculated on various types of domains, not limited to rectangular ones. The concept of double integration extends to more general regions, including non-rectangular domains, such as circles, triangles, and irregular shapes.
Double integrals are used to calculate the signed volume or area under a surface or over a region in two-dimensional space. While rectangular domains are often used for simplicity and ease of computation, they are not the only type of domain on which double integrals can be applied. In fact, double integrals can be evaluated on a wide range of regions as long as they satisfy certain conditions. These conditions include being bounded, connected, and having a well-defined boundary. The region can be defined by any shape, including circles, triangles, ellipses, polygons, or irregular curves. To calculate a double integral over a non-rectangular domain, appropriate coordinate transformations or changes of variables may be required. These transformations help to map the non-rectangular domain onto a rectangular one, allowing for the application of standard integration techniques. In conclusion, while rectangular domains are commonly used in double integrals, they are not the only option. Double integrals can be computed on a variety of domains, enabling the evaluation of integrals over non-rectangular regions.
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An online music store charges $1.50 for each song after you pay a $18 subscription fee. write a function that represents the arithmetic sequence. how many songs can you buy if you have $50 to spend?
The answer of 21 tracks is accurate since, once the membership cost has been paid, the store charges $1.50 by each song. Since the monthly charge is a one-time expense, it is deducted from the $50 price cap.
What are the different sorts of function?The characteristic that every input is associated to approximately one output defines a function as a relationship between a series of inputs but a set of allowable outputs. A mapping from Here to there B will only be a function if every piece in set A has one end and only the image in set B. Let A & B have been any two non-empty sets.
The number of songs that may be downloaded with the specified budget is then calculated by dividing the remaining balance by the price of each song. The outcome is an analytic sequence because each song's price is set. The outcome is then rounded down to the closest whole number, which in this example is 21.
1. Take the $50 budget and deduct the $18 membership fee:
$50 - $18 = $32
2. Take the leftover amount and divide it by the price of each song:
$32 ÷ $1.50 = 21.33
3. To the nearest full number, round down:
21 songs
As a result, you may purchase 21 tracks for $50.
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Hey guys please help!!
Answer:
SAS
Step-by-step explanation:
the lines in the middle of a segment mean that they are equal in length.
So OE = EB and AE = EC.
Now, since angle AEB and angle DEC are vertical angles, they are equal.
Therefore the triangles are equal by SAS
HELPPPPP PLEASEEE!!!!
Answer:
X= - 3
Step-by-step explanation:
Multiply both sides by 2 to remove the division on the LHS
3X - 15=8X
Move 3X to the RHS
-15 =8X - 3X
-15= 5X
Divide both sides by 5
-3 =X
\(\boxed{c.\:x\:=\:-3}\) ✅
\(\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\orange{:}}}}}\)
\( \frac{3x - 15}{2} = 4x \\ ⇢ 3x - 15 = 4x \times 2 \\ ⇢ 3x - 15 = 8x \\ ⇢ 3x - 8x = 15 \\ ⇢ - 5x = 15 \\ ⇢ x = \frac{15}{ - 5} \\ ⇢ x = - 3\)
\({ \bf{ \underbrace{To\:verify :}}}\)
\( \frac{3x - 15}{2} = 4x \\ ⇢ \frac{3 \times (- 3) - 15 }{2} = 4 \times - 3 \\ ⇢ \frac{ - 9 - 15}{2} = - 12 \\ ⇢ \frac{ - 24}{2} = - 12 \\ ⇢ - 12 = - 12 \\ ⇢ L.H.S.=R. H. S\)
Hence verified.
\(\large\mathfrak{{\pmb{\underline{\orange{Happy\:learning }}{\orange{.}}}}}\)
Angles A and B are complementary to each other. If m∠A = 41° and m∠B = (2x + 19)°, find the value of x.
x = 15
x = 11
x = 58
x = 30
Given that Angles A and B are complementary to each other, the numerical value of x is 15.
What is the numerical value of x?Complementary angles are angles that sum up to 90 degrees.
Given the data in the question;
Angles A and B are complementary to each other.Measure of angle A = 41°Measure of angle B = (2x + 19)°Since Angles A and B are complementary to each other, the sum of angle A and B is 90 degrees.
Measure of angle A + Measure of angle B = 90°
Plug in the given values and solve for x.
41 + (2x + 19) = 90
41 + 2x + 19 = 90
2x + 60 = 90
2x = 90 - 60
2x = 30
x = 30/2
x = 15
Given that Angles A and B are complementary to each other, the numerical value of x is 15.
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Answer: A is the answer
Step-by-step explanation: i took the test and got it right
If GI and JL are parallel lines and mZJKH = 70°, what is m<LKM
WILL GIVE BRAINLIEST
Answer:
70°
Step-by-step explanation:
Since m∠JKH and m∠LKM are verticle angles, they are equal to each other.
find f'(x) when f(x) = (x^2) - 2x. find the equation of the tangent line and the normal line at x=4
The derivate of a function f(x) is determinated as:
\(f^{\prime}(x)=\lim _{h\to0}\frac{f(x+h)-f(x)}{h}\)For the function
\(f(x)=x^2-2x\)First we have to determine de f ( x + h ) as follow:
\(f(x+h)=(x+h)^2-2(x+h)\)\(f(x+h)=x^2+2xh+h^2-2x-h^{}\)Then we calculate and simplify the coeficient in the first formula
\(\frac{f(x+h)-f(x)}{h}\)\(\frac{(x^2+2xh+h^2-2x-h^{})-(x^2-2x)}{h}\)\(\frac{x^2+2xh+h^2-2x-h^{}-x^2+2x}{h}=\frac{h^2+2xh-h}{h}\)\(\frac{h^2+2xh-h}{h}\text{ = }\frac{h(h+2x-1)}{h}=h+2x-1\)So the derivate is:\(f^{\prime}(x)=\lim _{h\to0}\frac{f(x+h)-f(x)}{h}=\lim _{h\to0}h+2x-1\)\(f^{\prime}(x)=0+2x-1\)\(f^{\prime}(x)=2x-1\)------------------------------------------------------------------------------------The equation of the tangent:
First you need to know that the derivate of a function is equal to the slope (m) of the tangent of this function
And the equation to thist tangent in a specific point will be find using the next formula:
\(y-f(x_0)=m(x-x_0)_{}\)We have to calculate the slope in the point x =4 using the derivate:
\(m=2x-1\)\(m=2(4)-1=7\)In the point x=4
Calculate the value of f(x0) substituting in the function the given point x:
\(f(4)=4^2-2(4)\text{ = }8\)Knowing that we put the value of m and f(x0) in the equation of the tangent:
\(y-8=7(x-4)_{}\)\(y-8=7x-28\)\(y=7x-28+8\)So the equation of the tangent in x= 4 is:\(y=7x-20\)---------------------------------------------------------------------------
The normal line
The slope of the normal line is the opposite of the slope of theu tangent in an espesific point:
\(m_n=-\frac{1}{m_t}\)So in this situation is:
\(m_n=-\frac{1}{7}\)The equation of the normal line is given by the next formula:
\(y-f(x_0)=m_n(x-x_0)_{}\)Replacing the data we obtain:
\(y-8=-\frac{1}{7}(x-4)_{}\)\(y-8=-\frac{1}{7}x+\frac{4}{7}\)So the equation of the normal line is:\(y=-\frac{1}{7}x+\frac{60}{7}\)Construction 3.17 which was EAV-Secure Prove the opposite - i.e. if G is not a PRG, then 3.17 cannot be EAV-secure. Let G be a pseudorandom generator with expansion factor ℓ. Define a private-key encryption scheme for messages of length ℓ as follows: - Gen: on input 1 n
, choose uniform k∈{0,1} n
and output it as the key. - Enc: on input a key k∈{0,1} n
and a message m∈{0,1} ℓ(n)
, output the ciphertext c:=G(k)⊕m. - Dec: on input a key k∈{0,1} n
and a ciphertext c∈{0,1} ℓ(n)
, output the message m:=G(k)⊕c. A private-key encryption scheme based on any pseudorandom generator. THEOREM 3.18 If G is a pseudorandom generator, then Construction 3.17 is a fixed-length private-key encryption scheme that has indistinguishable encryptions in the presence of an eavesdropper. PROOF Let Π denote Construction 3.17. We show that Π satisfies Definition 3.8. Namely, we show that for any probabilistic polynomial-time adversary A there is a negligible function negl such that Pr[PrivK A,Π
eav
(n)=1]≤ 2
1
+neg∣(n)
If G is not a PRG, then Construction 3.17 cannot be EAV-secure. This shows the contrapositive of Theorem 3.18.
To prove the opposite, we need to show that if G is not a pseudorandom generator (PRG), then Construction 3.17 cannot be EAV-secure (indistinguishable encryptions in the presence of an eavesdropper).
Let's assume that G is not a PRG. This means that there exists some efficient algorithm D that can distinguish the output of G from random strings with non-negligible advantage. We will use this assumption to construct an adversary A that can break the EAV-security of Construction 3.17.
The adversary A works as follows:
1. A receives a security parameter n.
2. A runs the key generation algorithm Gen and obtains the key k.
3. A chooses two distinct messages m0 and m1 of length ℓ(n).
4. A computes the ciphertexts c0 = G(k) ⊕ m0 and c1 = G(k) ⊕ m1.
5. A chooses a random bit b and sends cb to the challenger.
6. The challenger encrypts cb using the encryption algorithm Enc with key k and obtains the ciphertext c*.
7. A receives c* and outputs b' = D(G(k) ⊕ c*).
8. If b = b', A outputs 1; otherwise, it outputs 0.
We analyze the probability that A can distinguish between encryptions of messages m0 and m1. Since G is not a PRG, D has a non-negligible advantage in distinguishing G's output from random strings. Therefore, there exists a non-negligible function negl such that:
|Pr[D(G(k)) = 1] - Pr[D(U) = 1]| ≥ negl(n),
where U denotes a truly random string of length ℓ(n).
Now, consider the probability of A winning the PrivK game:
Pr[PrivK_A,Π
eav
(n) = 1] = Pr[b = b']
= Pr[D(G(k) ⊕ c*) = D(G(k))]
= Pr[D(G(k)) = 1]
≥ Pr[D(U) = 1] - negl(n).
Since negl(n) is non-negligible, we have:
Pr[PrivK_A,Π
eav
(n) = 1] ≥ 2^(-1) + negl(n).
Thus, if G is not a PRG, then Construction 3.17 cannot be EAV-secure. This shows the contrapositive of Theorem 3.18.
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Find the limit. Use l'Hospital's Rule if appropriate. If there is a more elementary method, consider using it.
lim ln(5x)/√5x
x→[infinity]
To find the limit of ln(5x)/√5x as x approaches infinity, we can use l'Hospital's Rule since it is an indeterminate form of ∞/∞.
Taking the derivative of the numerator and denominator separately, we get: lim [(1/5x) / (1/2√5x)] x→[infinity]
Simplifying this expression, we get: lim 2/5√5x x→[infinity]
Since the denominator approaches infinity as x approaches infinity, the limit is equal to 0.
Therefore: lim ln(5x)/√5x = 0 x→[infinity]
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A craftsman wants to build this fiddle. He needs to know the area of the face of the fiddle. How could he use the measurements shown to find the area?
The Area of Trapezium is 50, 267 mm².
We have,
base 1 = 224 mm
base 2 = 77 mm
Height = 334 mm
Now, Area of Trapezium
= 1/2 (Sum of parallel side) x height
= 1/2 (224 + 77) x 334
= 1/2 x 301 x 334
= 50, 267 mm²
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